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Unit 4: Consumer choice
In accordance with the APT programme the
objective of the lecture is to help You to:
gain an understanding of the basic postulates
underlying consumer choice: utility, the law of
diminishing marginal utility and utility-maximizing
conditions, and their application in consumer decision-
making and in explaining the law of demand;
by examining the demand side of the product
market, to learn how incomes, prices and tastes affect
consumer purchases;
understand how to derive an individual’s demand
curve;
understand how individual and market demand
curves are related;
understand how the income and substitution effects
explain the shape of the demand curve.
Required reading Mankiw, N.G. Principles of Microeconomics. 6th
edition. South-Western. 2009.
Chapter 21. The theory of Consumer Choice
Questions to be revised
Opportunity cost;
Marginal analysis;
Demand schedule, own and cross-price
elasticities of demand;
Law of demand and Giffen good;
Factors of demand: tastes and incomes;
Normal and inferior goods.
Consumer choice
Consumers choose the best bundle (combination) of goods they can afford.
The “best bundle” is selected in accordance with preferences and utility functions to represent them, indifference curves;
An “affordable” bundle is given by the budget constraint.
Utility
Utility is a measure of personal satisfaction with consumption of goods: U(X).
Total utility
X
U
0
Nonsatiation of consumption: More is preferred to less
Total Utility and Marginal Utility Total utility
X
U
0
X 0
MU Marginal utility Diminishing marginal utility: each extra unit of a good consumed, holding constant consumption of other goods, adds successively less to utility
Marginal utility of a good shows an increase in total utility due to infinitesimal increase in consumption of the good, provided that consumption of other goods is kept unchanged:
X
UMU
Indifference curves
A
B
x2
x1 0
Indifference curve shows all the
consumption bundles that yield a
particular level of utility.
A set of indifference curves
Indifference curves do not
intersect
According to nonsatiation
condition the bundles that lie
above a given indifference
curve are preferred to bundles
on or below it. In other words,
an indifference curve which is
more distant from the origin
corresponds to more preferable
consumption bundles.
Indifference curves
A C
E
I
II III
IV
B
D
x2
x1 0
The bundles which give the consumer the same level of
utility as A, are situated either in the II or in the IV sections.
An indifference curve is a decreasing correspondence
between quantity of a good x1 and quantity of the other
good (x2).
Indifference curves
A
C
B
x2
x1 0
Convexity: consumers prefer variety
Slope of indifference curve at a given bundle is given by the marginal rate of substitution at that bundle
Marginal rate of substitution (MRS) x2
x1 0
MRS shows the quantity of good 2 consumer must sacrifice to increase the
consumption of good 1 without changing her (his) utility:
Δx2
Δx1
When the quantity a good (x2) consumed becomes smaller and smaller the consumer who gives up with one and the same unit of the good (x2) has to gain increasingly larger amount of the other good (x1) so as the level of utility to be kept unchanged.
Marginal rate of substitution (MRS) x2
x1 0
Convex to the origin indifference curves:
Diminishing marginal rate of substitution
Δx2
Δx2
Δx11 Δx1
2
When the quantity a good (x2) consumed becomes smaller and smaller the consumer has to give up with increasingly larger amount of it to gain one and the same unit of the other good (x1) so as the level of utility to be kept unchanged.
Marginal rate of substitution (MRS) x2
x1 0
Convex to the origin indifference curves:
Diminishing marginal rate of substitution
Δx1 Δx1
Δx21
Δx22
Marginal rate of substitution (MRS) x2
x1 0
Convex to the origin indifference curves:
Diminishing marginal rate of substitution
MRS and Marginal Utility Utility of the consumer is fixed on an indifference curve. For the change in total utility with a movement along an indifference curve to be zero, the utility gain (ΔU) due to the increase in consumption of the first good (Δx1) should be equal in absolute value to the drop in utility (-ΔU) caused by the decrease in consumption of the other one (Δx2):
Rearrange to get:
Budget Constraint
Denote by p1>0 the price of good 1,
and p2>0 - the price of the 2nd good.
Denote by M⩾0 the amount of money a consumer has got.
Budget constraint (line) is a combination of quantities of goods 1 and 2 the consumer can just afford:
p1x1+ p2x2= M.
Budget Constraint
x2
x1 0
Budget Set:
p1x1 + p2x2 ⩽ M;
quantity of good 1: x1⩾0;
quantity of good 2: x2⩾0.
Budget Set
Budget Constraint
Budget constraint (line) is a combination of quantities of goods 1 and 2, that the consumer can just afford:
p1x1+ p2x2 = M,
or
Absolute value of the slope of budget constraint equals the relative price of the first good (with respect to the price of the second one): p1/p2.
Slope of the budget line measures the rate at which the market is willing to substitute good 1 for good 2.
The real (with respect to the price of the second good) income of the consumer gives an intercept of the budget constraint at the vertical axes: M/p2.
x2
x1 0
Budget Constraint: changing prices and wealth
Suppose that price of the
first good falls down Suppose that income of
consumer falls down
x2
x1 0
x2*
x1*
A
E
Consumer choice: Optimality
Point A:
Point E:
A consumer is intended to choose the best and affordable consumption bundle (combination of two or more goods).
2
2
1
1
P
MU
P
MU
2
1
2
1
P
P
MU
MU
2
1
2
1
P
P
MU
MU
2
2
1
1
P
MU
P
MU
Consumer’s optimal choice is the bundle X=(x1,x2) where MRS is equal to the slope of the budget constraint:
Market trade-off
is equal to
the utility trade-off required to maintain constant utility
Consumer choice: Optimality
Optimal consumer’s bundle: example
Quantity of a good
Good 1 Good 2
MU1 MU1/P1 MU2 MU2/P2
1 60 12 70 7
2 50 10 60 6
3 40 8 50 5
4 30 6 40 4
5 25 5 30 3
6 20 4 20 2
Assume that income of a consumer is M=55, price of the first good is P1=5, price of the second good is P2=10.
Optimal consumption bundle: example
Quantity of a good
Good 1 Good 2
MU1 MU1/P1 MU2 MU2/P2
1 60 12 70 7
2 50 10 60 6
3 40 8 50 5
4 30 6 40 4
5 25 5 30 3
6 20 4 20 2
2
2
1
1
P
MU
P
MU , the whole income is spent for the two goods.
Consumer choice: example (APT 2008)
The table below shows the quantities, prices, and
marginal utilities of two goods, fudge and coffee,
which Mandy purchases.
Fudge Coffee
Quantity of purchase 10 pounds 7 pounds
Price per pound $2 $4
Marginal utility of
last pound
12 20
Mandy spends all her money and buys only these
goods. In order to maximize her utility, should
Mandy purchase more fudge and less coffee,
purchase more coffee and less fudge, or maintain
her current consumption? Explain.
Consumer choice: example (APT 2002) The table below shows total utility in utils that a utility-maximizing consumer receives from consuming two goods: apples and oranges.
Apples Oranges
Quantity Total utility Quantity Total utility
0 0 0 0
1 20 1 30
2 35 2 50
3 45 3 65
4 50 4 75
5 52 5 80
Assume that apples cost $1 each, oranges cost $2 each, and the consumer spends the entire income of $7 on apples and oranges. A. Using the concept of marginal utility per dollar spent, identify the combination of apples and oranges the consumer will purchase. Explain your reasoning.
Consumer choice: example (APT 2002)
Apples Oranges
Quantity Total utility Quantity Total utility
0 0 0 0
1 20 1 30
2 35 2 50
3 45 3 65
4 50 4 75
5 52 5 80
Assume that apples cost $1 each, oranges cost $2 each, and the consumer spends the entire income of $7 on apples and oranges. B. With the prices of apples and oranges remaining constant, assume that the consumer’s income increases to $12. Identify each of the following. (i). The combination of apples and oranges the consumer will
now purchase.
Consumer choice: example (APT 2002)
Apples Oranges
Quantity Total utility Quantity Total utility
0 0 0 0
1 20 1 30
2 35 2 50
3 45 3 65
4 50 4 75
5 52 5 80
Assume that apples cost $1 each, oranges cost $2 each, and the consumer spends the entire income of $7 on apples and oranges. B. With the prices of apples and oranges remaining constant, assume that the consumer’s income increases to $12. Identify each of the following. (ii). The total utility the consumer will receive from consuming
the combination in (i).
Consumer choice: example (APT 2002)
Apples Oranges
Quantity Total utility Quantity Total utility
0 0 0 0
1 20 1 30
2 35 2 50
3 45 3 65
4 50 4 75
5 52 5 80
Assume that apples still cost $1 each. C. With income remaining at $12, assume the price of oranges increases to $4 each. Identify each of the following. i. The combination of apples and oranges the consumer will
now purchase. ii. The total utility the consumer will receive from consuming
the combination in (i).
Adjustment to price changes: Slutsky price effect decomposition
Adjustment to price changes can be
decomposed into two effects: income effect and
substitution effect:
Due to substitution effect provided fixed
personal welfare an individual increases
consumption of the goods that become relatively
cheaper and reduces consumption of the goods
that become relatively more expensive.
Income effect is a variation of purchasing power
of a consumer’s income caused by a fall or a rise
in commodity prices.
CPIE
OPSE
Adjustment to price changes: income effect and substitution effect (normal goods)
x2
x1 0 x11
E1
E2
E3
x13 x1
2
x21
x22
x23
OPIE
CPSE
Assume that price of
the 1st good goes down
OPSE, CPSE – own- and
cross-price substitution effects
OPIE, CPIE – own- and
cross-price income effects
CPIE
OPSE
Adjustment to price changes: income effect and
substitution effect (inferior but not Giffen goods) x2
x1 0 x11
E1
E2
E3
x13 x1
2
x21
x22
x23
OPIE
CPSE
Assume that price of
the 1st good goes down
OPSE, CPSE – own- and
cross-price substitution effects
OPIE, CPIE – own- and
cross-price income effects
CPIE
OPSE
Adjustment to price changes: income effect and substitution effect (Giffen goods)
x2
x1 0 x11
E1
E2
E3
x13 x1
2
x21
x22
x23
OPIE
CPSE
Assume that price of
the 1st good goes down
OPSE, CPSE – own- and
cross-price substitution effects
OPIE, CPIE – own- and
cross-price income effects
Individual demand curve – quantity demanded of a
good at every possible price of this good, keeping
everything else (prices of other goods and income
of consumer) fixed.
Adjustment to price changes: individual demand curve
x2
0 x12
E1
E2
x11
x21
x22
x1 p2
x2
p21 p2
2
x21
x22
0
Assume that price of the 2nd good goes down
Adjustment to income changes: Engel curve (normal good)
x2
0 x12
E1
E2
x11
x21
x22
x1 M
x2
M2 M1
x21
x22
0
Assume that the consumer’s income goes up
Adjustment to income changes: Engel curve (inferior good)
x2
0 x12
E1
E2
x11
x21
x22
x1 M
x2
M2 M1
x21
x22
0
Assume that the consumer’s income goes up
For any good (normal or inferior) substitution effect leads to reduction in quantity demanded in response to increase in own price.
For inferior good income effect leads to increase in quantity demanded in response to increase in own price.
Giffen good – an inferior good, for which income effect dominates substitution effect. Quantity demanded increases in response to increase in own price!
Adjustment to price changes
Adjustment to price changes: inferior but not Giffen good
0 x12
E1 E2
x11
x21
x22
x1
p1
x2
p11
p12
x11 x1
2 0
x13
x1
E3 x23
Assume that price of
the 1st good goes down
OPSE – own-price
substitution effect
OPIE – own-price
income effect OPSE
OPIE
Demand curve
Adjustment to price changes: Giffen good
0 x12
E1
E2
x11
x21
x22
x1 p1
x2
p11
p12
x12 x1
1 0
x13
x1
E3 x23
Assume that price of
the 1st good goes down
OPSE – own-price
substitution effect
OPIE – own-price
income effect OPIE
OPSE
Demand curve
(an exception of
the law of demand)
Market demand curve
quantity
price
0
10
12
6 8
Consumer 1 Consumer 2
With a large number of consumers one can get a smooth curve
Market demand
14
A sum of quantities demanded by all consumers at each price (a “horizontal” sum of individual demand curves for a
particular good )
Suppose, there are 2 consumers with individual demand curves:
Consumer 1: P=12-2Q1;
Consumer 2: P=10-1.25Q2.
Adjustment to price changes: example (APT 2009)
Sasha is a utility-maximizing consumer who spends all
of her income on peanuts and bananas, both of which
are normal goods.
(a) Assume that the last unit of peanuts consumed
increased Sasha’s total utility from 40 utils to 48 utils and
that the last unit of bananas consumed increased her
total utility from 52 utils to 56 utils.
(i) If the price of a unit of peanuts is $1 and Sasha is
maximizing utility, calculate the price of a unit of
bananas.
(ii) If the price of a unit of peanuts increases and the
price of a unit of bananas remains unchanged from
the price you determined in part (a)(i), how will
Sasha’s purchase of peanuts change?
Adjustment to price changes: example (APT 2009)
Sasha is a utility-maximizing consumer who spends all
of her income on peanuts and bananas, both of which
are normal goods.
(b) Assume that the cross-price elasticity of demand
between peanuts and bananas is positive. A widespread
decease has destroyed the banana crop. What will
happen to the equilibrium price and quantity of peanuts
in the short run? Explain.
(c) Assume that the price of bananas increases.
(i) Will the substitution effect increase, decrease, or
have no effect on the quantity of bananas
demanded?
(ii) What will happen to Sasha’s real income?